We present a theor of linear and quadratic time-frequency representations (&FRs) that are covariant to time-frequency displacement operators. The theory unifies important T F R classes (short-time Fourier transform, wavelet transform; Cohen’s, affine, hyperbolic, and power classes), and it allows the systematic construction of new TFRs that are covariant to a given operator.

Most of signals in engineering are nonstationary and time-varying. The Fourier transform as a traditional approach can only provide the feature information in frequency domain. The time-frequency techniques may give a comprehensive description of signals in time-frequency planes. Based on some typical nonstationary signals, five time-frequency analysis methods, i.e., the short-time Fourier tran...

Energy concentration of the S-transform in the time-frequency domain has been addressed in this paper by optimizing the width of the window function used. A new scheme is developed and referred to as a window width optimized S-transform. Two optimization schemes have been proposed, one for a constant window width, the other for time-varying window width. The former is intended for signals with ...

This paper discusses the applicability of the Wavelet transform for analyzing an EMG signal and discriminating motion classes. In many previous works, researchers have dealt with steady EMG and have proposed suitable analyzing methods for the EMG, for example FFT and STFT. Therefore, it is difficult for the previous approaches to discriminate motions from the EMG in the different phases of musc...

Shape is one of the primary features in Content Based Image Retrieval (CBIR). Many shape representations and retrieval methods exist. However, most of those methods either do not well capture shape features or are difficult to do normalization (or matching). Among them, methods based Fourier descriptors (FDs) achieve both good representation and easy normalization. FDs is often blamed for not b...

Time-frequency concentration operators restrict the integral analysis-synthesis formula for short-time Fourier transform to a given compact domain. We estimate how much corresponding eigenvalue counting function deviates from Lebesgue measure